Pinchas Zukerman was teaching a master class at Julliard and decided that he could drive a point home to some Asian students by telling them Koreans don't sing.
“Sometimes if you have a question about how to play it, sing it,” he said. “I know in Korea they don’t sing.” He went on to talk about how wrong it is, that in Korea they don’t sing.
One of the sisters spoke up, “But I’m not Korean,” she said.
“Then where are you from?”
She began to explain that she’s of half Japanese descent, then he interrupted, “In Japan they don’t sing either.” He mimicked a sing-song vocal style that has been stereotyped as Asian. “That is not singing. Violin is not a machine.”
So there is a lot going on here. Two big issues that I think I see are first, assuming someone's culture or identity based on perceived genetic markers, and second, generalizations and misinformation about entire cultures.
To the first issue, and I didn't look at the source material so I don't know, but if you are at a school or workplace in America and you are asking someone "where are you from?" because they don't look "American", you should probably rethink what you're about to say. The answer is just as likely to be Springfield MA as it is "Exotic Foreign Country". Also, assuming a culture, which is different again from both origin and genetic background, is not a good idea. I have been friends with adopted people of Korean descent who have no knowledge or ties (or desire to become acquainted with) with the Korean culture, and I know some American kids here in Japan who attend Japanese public school full time for their education, are more or less fluent, and nearly all their friends are Japanese. Who can say what someone's culture is based on their looks? It is always complex. This isn't to say that it is NEVER appropriate to comment on someone else's culture -- if someone I meet is speaking Korean or Japanese, or says they are from XYZ country, I feel fine saying "oh, I love XYZ country! Are you from there?". And I can have a great conversation.
To the second issue...
In Japan, many if not most of the people I've met have the ability to sing well and accurately, and Karaoke is one of the most popular pastimes.
I got to play with some amazing singers and singing groups when I lived in Korea.
Compare to the US where I'd argue a majority of people, myself included, are only brave enough to sing in the shower.